Metamath Proof Explorer


Theorem e112

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e112.1
|- (. ph ->. ps ).
e112.2
|- (. ph ->. ch ).
e112.3
|- (. ph ,. th ->. ta ).
e112.4
|- ( ps -> ( ch -> ( ta -> et ) ) )
Assertion e112
|- (. ph ,. th ->. et ).

Proof

Step Hyp Ref Expression
1 e112.1
 |-  (. ph ->. ps ).
2 e112.2
 |-  (. ph ->. ch ).
3 e112.3
 |-  (. ph ,. th ->. ta ).
4 e112.4
 |-  ( ps -> ( ch -> ( ta -> et ) ) )
5 1 vd12
 |-  (. ph ,. th ->. ps ).
6 2 vd12
 |-  (. ph ,. th ->. ch ).
7 5 6 3 4 e222
 |-  (. ph ,. th ->. et ).